Polyglottic Euler in 5 Lambdas

Polyglottic attempts to euler in Clojure, Common Lisp (SBCL), Racket, Julia, SML and Haskell. The codes will be refactored from time to time without deleting old codes.

Note: The logo was taken from This blog. Unfortunately nobody noticed that the Johnnie posture is lambda-shaped :)

The Eulerians:

About the Lisps

"Lisp is worth learning for the profound enlightenment experience you will have when you finally get it; that experience will make you a better programmer for the rest of your days, even if you never actually use Lisp itself a lot."
~ Eric Raymond, "How to Become a Hacker"

Rationales

The need for benchmark for a particular euler problem in terms of speed
Encouragement for others to come up with faster/better solutions
PE problems are good practice for optimising codes, which is critical skill in the era of big-data
Finding interesting ideas for creating problems :)

In every source code, time-elapsed for each solution will be listed.

Performance Comparison on MBA i7 1.7GHz

Implementations:

Clojure using Clojure (Mostly 1.7) on JDK 1.8 (Also used for Java)
Clojurescript on NodeJS
Common Lisp using SBCL 1.2.x
Haskell using GHC compiled using -O2 optimisation
SML using SMLNJ & MLTON (take the faster one, although in general MLTON is much faster)
Racket mostly using Racket 6.1.x and Typed Racket
C using whatever there is on Macbook, optimized to the max using -Ofast
Julia using Julia 0.3.x (soon to be upgraded to 0.4)
Python using pypy
F3 using Mono on Mac

Problem no 1

Prob: Find the sum of all multiples of 3 or 5 that less than 1000

Clojure averaging 3.2 msecs
Clojure 1.7 0.08ms
SBCL averaging 0.3 msecs
Haskell 0.07ms Racket less than 1 msec
Java benchmark 0.05ms
C benchmark 0.05ms
Swift 0.018ms
Julia 0.008ms NEW RECORD!
Elixir 0.1ms F# less than 1ms
SML 0.016ms
Pypy 0.027ms
Mathematica 2ms

Problem no 2

Prob: Find the sum of even-valued fibo numbers less than 4,000,000

Clojure 0.08 msecs
Clojure 1.7 0.04ms
SBCL less than 0.01 msecs
Haskell 0.06ms
Racket less than 1 msec
C Benchmark 0.03ms
Java benchmark 0.005ms
Swift 0.004ms
Julia 0.004ms TIGHT with SWIFT!
Pypy 0.02ms
Elixir 0.008ms
Mathematica 0.08ms

Problem no 3

Prob: Find the largest prime factor of 600851475143

Clojure 32 msecs
Type hinted Clojure using transient and unchecked-math 5-6msecs
Further optimised type-hinted Clojure 0.3-0.4ms
SBCL 37-42 msecs
Type hinted SBCL 4-6ms
Further optimised SBCL 0.45ms
Haskell 0.5ms
SML 2 ms
Racket 50-60 ms
Typed Racket 6ms
Further optimised Typed Racket 0.4-0.5ms
C as benchmark 0.2ms
Java as benchmark 5ms
Java v2 0.02ms
Swift 0.11ms NEW RECORD!!
Julia 0.16ms
Juliabox-0.4 v2 0.043ms
Juliabox-0.4 v3 0.019ms
Pypy 1.5ms
Elixir 3.5ms
F# less than 0.5 ms
Mathematica 3.4ms

Problem no 4

Prob: Find the largest palindrom that is a product of two 3 digits number (can be different numbers).

Clojure 16-18 msecs
Clojure with memoization 0.01ms
SBCL 11-20 msecs
Haskell 4ms
SML 1.3 msec
Java 2ms
Julia 0.006ms FAST! (using memoization)
Pypy 5.5ms
F# 1ms
Mathematica 16ms

Problem no 5

Prob: Find the smallest number that can be evenly divided by all integers from 1 to 20.

Clojure 0.1 ms
SBCL 0.006 ms
Haskell 0.07ms
Julia 0.005ms
Pypy 0.07ms
SML 0.006ms
Java 0.004ms
Racket less than 0.5ms
F# less than 0.5ms
Mathematica 0.034ms

Problem no 6

Prob: Calculate the difference between the sum of squares of the first 100 natural numbers and the square of sum those numbers.

Clojure 0.3-0.4 msecs
SBCL 0.01 msecs
Haskell 0.1ms
Julia 0.004ms
Pypy 0.4ms
Java 0.005ms
F# less than 1ms
SML 0.007ms
Mathematica 0.12ms

Problem no 7

Prob: Find the 10,001st prime

Clojure 40-50 msecs
Type-hinted Clojure 30-50 ms
Type-hinted Clojure using sieve 5-8ms
Type-hinted Clojure 1.7 using transducers 0.4ms
SBCL 90-110 msecs
Type hinted SBCL 24ms
Type-hinted SBCL using sieves 2ms
Typed Racket 35-38ms
Typed Racket using sieve 1-2ms
Haskell 25ms
SML 17 msecs
C Benchmark using sieve 0.9ms
Swift naive using Int32 10ms
Swift using sieves 0.7ms
Java 1.2ms
Julia using sieves 0.7ms
Pypy 6ms
SML 1ms
F# less than 0.5ms

Problem no 8

Prob: Find the largest product of 13 digits in a 1000 digits series

Clojure 45-65 msecs
Clojure 1.7 3ms
SBCL 23 msecs
Haskell 3ms
Julia 0.7ms
F# 3ms

Problem no 9

Type-hinted Clojure 3-4ms
Further optimised Clojure 0.4ms
Crazy clojure technique 0.06ms
Type-hinted SBCL 3ms
Typed Racket 1ms
Haskell 13ms
SML 1 ms
C as benchmark 0.25ms
Java benchmark 2.5ms
Java v2 1.1ms
Swift 0.32 ms
Julia 0.006ms
Pypy 0.03ms

Problem no 10

Prob : The sum of all positive primes that less than 2,000,000

Clojure 2,500 msecs (2.5 secs)
Type Hinted Clojure using unchecked-math 1,165 msecs
Typed Hinted Clojure naive using clojure-1.7 pmap-reducers 360ms (FASTEST for non-sieve)
Type-hinted Clojure using sieves 120-140ms
Type-hinted Clojure 1.7 sieve using reducers 15ms!!
Clojure 1.7 sieve 6ms!! FASTEST!!
SBCL 3,269ms in SBCL 1.2.2
Type hinted SBCL 1,236ms
The same type hinted version in 32bit windows runs in 832ms
Type-hinted SBCL using sieves 21ms
Haskell 1,320 msecs (1.3 secs)
Haskell on Win32 470 msecs
SML 736 msecs!! (0.736 secs)
SML sieve 18ms
Java sieve 6.3ms
Racket 4-6K msecs
Typed Racket 2,200 msecs (Faster than Clojure)
Typed Racket in Win32 987 msecs
Typed Racket using sieves 29ms
C Benchmark using sieve 24 ms
Swift naive 1,421ms
Swift sieves 16ms
Julia using sieves 9ms
Pypy 75ms
F# 7ms

Problem no 12

Prob: Triangle number that has more than 500 factors

Clojure 1,700 ms
Type hinted Clojure 560 ms
Clojure v2 using memoized 13ms
SBCL 2,400 ms
Type hinted SBCL 590 ms
SBCL v2 21 ms
SBCL v3 sieve-like 8ms
SBCL using proto-memoize 1ms
Typed Racket 1000 ms
Racket v2 42 ms
Haskell compiled 660 ms
Haskell v2 30ms
SML 730ms
SML v2 9.5 ms
C Benchmark 580 ms
C Benchmark v2 6 ms
C Benchmark proto-memoize 3 ms
Java Benchmark 11 ms
Java v2 1.2ms
Swift 7ms
Julia 9ms Julia v2 0.2ms
F# 7ms

Problem 13

Clojure 1.3ms
Haskell 3ms
Julia 0.3ms

Problem no 14

Problem : Longest collatz sequence that started from n below 1million

Clojure 5.3 seconds
Type hinted Clojure 1.2-1.3 seconds
Type hinted Clojure using memoize 0.8-0.9 second
Type hinted Clojure starting 500,000 and odd-numbers only using memoize 168ms
SBCL 29-32 seconds
Type hinted SBCL 5 seconds
Type hinted SBCL 1.4 sec
Haskell compiled 4.36 seconds
Typed Racket 3.3 seconds (even better than Haskell)
Typed Racket 0.9 second (check >500k odds only)
SML 36 seconds
SML MLTON 627ms
C as benchmark (starting from half a million and check odd only) 179ms
Java 55ms
Swift 185ms
Julia 800ms
Julia v2 39ms
F# with Dynamic programming 471ms

Problem no 15

Clojure 0.14 msec
SBCL 0.018 msec
Haskell 0.08ms
Julia 0.07ms
SML 0.012ms
F# less than 0.5ms

Problem no 16

Clojure 1.3ms
Julia 0.8ms
Haskell 0.2ms
Pypy 2ms
F# 1ms

Problem 17

Julia 2ms
Haskell 1ms

Problem 18

Clojure 1ms
Julia 0.2ms
Haskell 1ms
F# less than 0.5ms

Problem 19

Haskell 1ms

Problem no 20

Clojure 0.7ms
Julia 0.4ms
Haskell 0.1ms
F# less than 0.5ms

Problem no 21

Problem : The sum of all amicable numbers less than 10,000

Clojure 72 ms
Type hinted Clojure 17-22 ms
Clojure 1.7 11ms
Clojure v2 2.4ms
SBCL 51 ms
Type hinted SBCL 17-20 ms
Haskell compiled 30 ms
Typed Racket 24ms
SML 7ms
Java benchmark 14ms
Java 2.2ms
C as benchmark 7ms
C using dynamic programming 4.5ms
Julia 7ms
Juliabox v2 1.3ms
F# using list 5ms, and 4ms using loop
F# v2 less than 1ms

Problem 22

Haskell 90ms
Julia 23ms
F# 108ms

Problem 23

Problem : The sum of all integers that cannot be written as the sum of two abundant numbers

Type-hinted Clojure 240-250ms
Clojure 1.7 110ms
Clojure 1.7 v2 50ms
Type-hinted SBCL 275ms
SBCL sieve-like 102ms
Typed Racket 450-460ms
Haskell 14 seconds
C as benchmark 128ms
Julia 230ms
Julia v2 on Juliabox-0.4 runs in 25ms
SML MLTON 132ms
F# 102ms
F# v2 27ms

Problem 24

Problem: Very nice problem, highly recommended!!

Clojure 0.23 msec
SBCL 0.02 msec
Haskell 1 msec
Julia 0.07ms
SML 0.007ms

Problem no 25

Prob: Find the first fibo element that reach 1000 digits.

Clojure averaging 2.9 msecs
Type hinted Clojure using unchecked-math < 1 ms
SBCL averaging 1.3 msecs
SBCL One-liner 1ms
Racket 3-4 msecs
Typed Racket 1 ms
Haskell averaging 10 msecs
Haskell 0.8ms
SML 36 msecs (SML LargeInt is not efficient)
SML MLTON 1.5ms
Julia 4ms
F# 1ms

Problem no 26

Prob: Very nice problem, find the max recurring digits of recyprocal 1/d where d < 1

Type-hinted Clojure 0.5-0.6ms
Type-hinted SBCL 1.2ms
Typed Racket 0.6-0.8ms
Haskell 11ms
SML 0.4-0.6ms
C as benchmark 0.12ms
Python for benchmark 8.7ms
Julia 0.07ms

Problem 27

Prob: Pretty complex to write here

Clojure 27-28ms
SBCL 36-38ms
SBCL using proto-memoize 10ms
Haskell 80ms
SML 3,290ms (Very sloow)
C as benchmark 20ms
Julia 41ms

Problem 28

Prob: Some fun stuffs

Clojure 0.082ms
SBCL 0.023ms
Haskell 0.4ms
C as benchmark 0.042ms
Julia 0.03ms

Problem 29

Clojure 0.065 msec
SBCL 0.019 msec
Haskell (one liner) 1.2 sec
SML 2.4 sec (Very inefficient sml)
Julia 15ms

Problem no 30

Clojure 730ms
Parallel mapping Clojure 92ms
Type-hinted SBCL 820ms
Haskell compiled 320ms
New version Haskell 170ms
SML 1,620ms
SML new version 315ms
C Benchmark 287ms
Julia 19ms

Problem 31

Problem : How many ways we can write 200 as the sum of coins 1,2,5,10,20,50,100,200

Clojure using memoization 7.2ms & 0.1ms for subsequent calls
Clojure without memoization 3ms
Racket without memoization 5ms
Haskell 4ms
SBCL 4ms
SML 3ms
C Benchmark 0.5ms
Julia 17ms

Problem 32

Prob: axb = c where a++b++c pandigital 1-9

Clojure 120ms
Common Lisp 57ms
Haskell compiled 19 sec
Haskell v2 ~60ms
SML 77ms

Problem 33

SBCL 0.8 msec
Clojure 18ms
Julia 17ms

Problem 34

Prob: find the sum of all numbers that are equal to the sum of factorials of their digits

SBCL 0.76 sec
Haskell compiled 0.46sec & 5.3 sec depends on limit
SML 0.349 & 1.349 depends on limit
Julia 11ms

Problem no 35

Prob: how many circular primes exist under 1000000

Clojure 56ms
Clojure using parallel map 21ms
SBCL 1,460ms
Common Lisp (SBCL) v2 22ms
SBCL proto-memoize 12ms
Haskell compiled 550ms
Haskell v2 20-30ms
SML 360ms
SML v2 10-12ms
C as benchmark 10ms
Julia 17ms

Problem no 36

Prob: find the sum of all numbers that are palindrome in both decimal and binary bases

Clojure 45-54ms
SBCL 4,700 ms
SBCL v2 3ms
Haskell 770ms
Haskell v2 2.6ms
SML 860ms
SML v2 ~1ms
Julia 1.3ms

Problem no 37

SBCL 1,580ms
SBCL v2 ~1ms
SBCL proto-memoize 0.4ms
Clojure 1,500ms
Clojure v2 1.3-2.5ms
Haskell 720ms
Haskell 0.5ms
SML ~1ms
Julia 2ms

Problem 38

SBCL 0.1ms
Clojure 1-2ms
Haskell 0.2ms
SML < 1ms
Julia 0.08ms

Problem no 39

SBCL 8ms
SBCL v2 0.3ms
Clojure 12ms
Clojure v2 2-3ms
Haskell 10ms
Haskell bruteforce 40ms
Julia 22ms

Problem no 40

SBCL tricky version 0.2ms
C benchmark tricky version 0.045ms
Java benchmark tricky version 0.054ms
Haskell 10ms
Clojure 31ms
Julia 0.03ms

Problem no 41

Problem : The sum of all pandigital primes

Haskell (one liner) 10ms
Clojure 2ms (fast)
Common Lisp 0.15ms (Uberfast!)
Julia 1.3ms

Problem 42

Haskell 10ms

Problem 43

Substring divisibility

SBCL 0.5ms
Julia 1ms
Haskell 51ms

Problem 44

Laziness stuff

Clojure (using pmap) 0.21 sec
Haskell (optimized to the max) 0.23 sec
Julia 41ms

Problem 45

Clojure 0.1ms
C as benchmark 0.3ms
Julia 0.7ms

Problem 46

Clojure 2.5ms
Haskell 2.5ms
Julia 22ms

Problem 47

Clojure 180ms
SBCL 98ms
C as benchmark 58ms
Julia 220ms

Problem 48

Clojure 3.6ms
Haskell 4.3ms
SBCL 4ms
Julia 1.7ms

Problem 49

SBCL 0.3 ms
Julia 1.5ms
Haskell 1.4ms

Problen no 51

Haskell 320ms

Problem 52

Problem : What is the smallest number where n,2n,3n,4n,5n,6n contain the same digit with different order

Clojure (1.7) 201ms
Julia 76ms

Problem 53

Clojure 1.7 (bruteforce) 2ms
Julia 0.8ms

Problem 55

Julia 28ms

Problem 56

Julia 11ms

Problem 57

Julia 98ms

Problem 58

Julia 0.4sec

Problem 59

Julia 76ms

Problem 62

Clojure 43ms
SBCL 820ms
Julia 24ms
F# 30ms

Problem 63

Prob : How many a^m have m digits?

SBCL 0.1 ms
Clojure 0.4 ms
Julia 0.07ms

Problem 65

SBCL 0.3ms
Julia 1.3ms

Problem 67

Clojure 1.7 15ms
Haskell 26ms
Julia 4ms
F# 1ms

Problem 69

Julia 0.1ms

Problem 71

Julia 0.03ms Haskell less than 1ms

Problem 72

Julia 102ms
F# 53ms

Problem 73

Julia 1.2sec

Problem 75

Problem : How many L <= 1,500,000 that can form a right-triangle only once.

SBCL 0.2second
Clojure 1.7 61ms
Julia 47ms

Problem no 76

Problem : How many ways 100 can be written as the sum of positive integers

Clojure 0.05ms (memoization)
SBCL 5600ms
Haskell 2,300ms
Julia 6ms

Problem 77

Problem : which number can be express as the summation of primes in 5000 different ways

SBCL 4ms
Clojure 6ms

Problem 80

SBCL 223ms

Problem 82

Clojure 1.7 8ms

Problem 81

Julia 8ms

Problem 84

Clojure 600ms

Problem no 85

Clojure 1.5 sec
SBCL 0.53 sec
Julia 11ms

Problem 87

Julia 0.72sec

Problem 90

Clojure 3secs

Problem 92

Julia 98ms

Problem 93

Clojure 500ms

Problem 95

Julia 178ms

Problem 98

Clojure 300ms

Problem 99

Julia 2ms

Problem no 100

Clojure 0.039 msec
SBCL 1.2 msec

Problem 101

Racket 6ms (Need to use matrix-solve)

Problem 103

Clojure 47ms

Problem 107

Clojure 30ms

Problem 108

Julia 16ms

Problem 110

Clojure 47ms

Problem 111

Clojure 480ms

Problem 113

Clojure 12ms
Julia 6ms

Problem 114

Clojure 20ms

Problem 115

Clojure 0.3ms

Problem 116

Clojure 0.6ms
SBCL 0.1ms
Julia 1.6ms

Problem 117

Julia 7ms

Problem 118

Clojure 14secs

Problem 119

Julia 0.4ms

Problem 123

Julia 234ms

Problem no 125

Clojure 0.5 sec
SBCL 0.6-0.8 sec

Problem no 129

Clojure 52ms
Julia 35ms

Problem no 130

Clojure 219ms
Julia 97ms

Problem no 131

SBCL 3ms
Haskell interpreted 230ms

Problem no 136

Julia 3.6sec

Problem no 139

Clojure 12sec
Julia 2sec

Problem 148

Clojure 0.1ms

Problem 150

Clojure 44sec

Problem 159

Clojure 213ms
Julia 1.56sec

Problem 164

Clojure 0.3ms

Problem no 169

Clojure 1ms (memoized)

Problem no 173

Clojure 0.163 sec
Clojure loop version 32ms
Haskell 8.3 sec
Julia 23ms
Julia v2 2ms
F# 2ms

Problem no 174

Clojure 1.2 sec
Clojure v2 64ms
Julia 36ms
Julia-0.4 v2 18ms
F# 10ms

Problem 179

Julia 1.8sec

Problem 183

Clojure 67sec

Problem 187

Julia 498ms
Clojure 1272ms

Problem 188

Clojure 1.7ms
Julia 6ms

Problem 191

Clojure 11ms
Julia 0.5ms

Problem 204

Haskell 890ms

Problem 211

Racket 393secs

Problem 215

Clojure 249ms (once the crack matrix has been built)

Problem no 234

Clojure 2.3 sec
SBCL 1.4 sec

Problem 249

Clojure 1001seconds

Problem 286

Clojure 98ms

Problem 297

Clojure 39ms

Problem 315

Clojure 12secs

Problem 303

Clojure 57sec

Problem 345

Clojure 1.1sec

Problem 346

Clojure 2.6sec

Problem 347

Clojure 1.2sec

Problem 348

Clojure 10secs

Problem 381

Clojure 23 secs

Problem 387

Clojure 2 secs

Problem 401

Clojure 33 secs
Haskell 26 secs

Problem 429

Clojure 9.3sec

Problem 491